How can current quantum computers solve complex industrial optimization problems that far exceed the qubit capacity of a single processor?This use case demonstrates a scalable hybrid quantum-classical pipeline for thousand-variable constrained optimization. Applied to Minimum Birkhoff Decomposition (MBD)—a challenge in network scheduling, optical switching, and energy trading—our approach combines spectral graph partitioning, shallow QAOA sampling, classical feasibility repair, and Extended Fully-Corrective Frank-Wolfe (E-FCFW) optimization.We validated the framework on the 1,354-bus PEGASE transmission grid benchmark, a 1,710-variable problem requiring 1,710 qubits without partitioning. Using spatial circuit packing on 156-qubit IBM Heron processors, independent subproblems run concurrently, achieving a 3x reduction in QPU execution time. Hardware results prove that repaired QAOA samples deliver lower residual error than simulated annealing and random sampling baselines.This work provides a proven blueprint for deploying quantum sampling on large-scale industrial problems today. We invite network operators, energy companies, logistics providers, and quantum researchers interested in scaling hybrid algorithms for real-world applications to reach out and collaborate!
